By now in this chapter, you have practiced multiplying, dividing, adding, and subtracting fractions. The following table summarizes these four fraction operations. Remember: You need a common denominator to add or subtract fractions, but not to multiply or divide fractions
Summary of fraction operations
Fraction multiplication: Multiply the numerators and multiply the denominators.
$\frac{a}{b}\xb7\frac{c}{d}=\frac{ac}{bd}$
Fraction division: Multiply the first fraction by the reciprocal of the second.
Fraction addition: Add the numerators and place the sum over the common denominator. If the fractions have different denominators, first convert them to equivalent forms with the LCD.
$\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$
Fraction subtraction: Subtract the numerators and place the difference over the common denominator. If the fractions have different denominators, first convert them to equivalent forms with the LCD.
$\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}$
Simplify:
ⓐ$-\frac{1}{4}+\frac{1}{6}$
ⓑ$-\frac{1}{4}\xf7\frac{1}{6}$
Solution
First we ask ourselves, “What is the operation?”
ⓐ The operation is addition.
Do the fractions have a common denominator? No.
$-\frac{1}{4}+\frac{1}{6}$
Find the LCD.
Rewrite each fraction as an equivalent fraction with the LCD.
Simplify the numerators and denominators.
$-\frac{3}{12}+\frac{2}{12}$
Add the numerators and place the sum over the common denominator.
$-\frac{1}{12}$
Check to see if the answer can be simplified. It cannot.
ⓑ The operation is division. We do not need a common denominator.
$-\frac{1}{4}\xf7\frac{1}{6}$
To divide fractions, multiply the first fraction by the reciprocal of the second.
Use the order of operations to simplify complex fractions
In
Multiply and Divide Mixed Numbers and Complex Fractions , we saw that a complex fraction is a fraction in which the numerator or denominator contains a fraction. We simplified complex fractions by rewriting them as division problems. For example,
Questions & Answers
can someone help me with some logarithmic and exponential equations.
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.